where \(c_s\)  represents the speed of sound and \(\gamma \)  is a fluid dependent constant. We take \(\gamma =7/5\)  for air in typical atmospheric conditions. We consider the Sod Shock tube [1]}, [2]}, [3]} with initial conditions
\(\rho (x,0) ={\left\lbrace \begin{array}{ll}1.0 & \quad x < 0.5 \\0.125 & \quad x \ge 0.5 \\\end{array}\right.}\qquad \rho u(x,0) = 0,\qquad E(x,0) = \frac{1}{\gamma - 1}{\left\lbrace \begin{array}{ll}1.0 & \quad x < 0.5 \\0.1 & \quad x \ge 0.5 \\\end{array}\right.}\) 
